Draw the graph of y = x3 + 3 for –3 ≤ x ≤ 3. Use your graph to find
a) the value of y when x = 2.5
b) the value of x when y = –15
a) When x = 2.5, y ≈ 18.6
b) When y = –15, x ≈–2.6
Plot the graph of y = x3 – 9x + 5 for –4 ≤ x ≤ 4 and use your graph to find:
a) the value of y when x = 1.6
b) the value of x when y = 12
a) When x = 1.6, y ≈ –5.3
b) When y = 12, x ≈ –0.8, or x ≈ –2.5
How to graph cubic functions using a calculator or technology?
We can graph cubic functions by transforming the basic cubic graph. The basic cubic graph is y = x3.
For the function of the form y = a(x − h)3 + k.
If k > 0, the graph shifts k units up; if k < 0, the graph shifts k units down.
If h > 0, the graph shifts h units to the right; if h < 0, the graph shifts h units left.
If a < 0, the graph is flipped.
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